We examine the risk neutral probability density (RND) for the S&P 500 extracted from real-time bid and ask quotes for index options, under extreme market stress during the fall of 2008. The RND provides exceptional detail about investors' expectations as intraday volatility increased to a level...

Standard approaches to designing a futures hedge often suffer from two major problems. First, they focus only on minimizing risk, so no account is taken of the impact on expected return. Second , in estima ting the hedge ratio, no allowance is made for time variation in the distribution of cash...